Cloud Structure on Venus with VIRTIS
J. K. Barstow
September 28, 2009
First Year Report
Lady Margaret Hall
Atmospheric, Oceanic and Planetary Physics, University of Oxford
∼ 12500 words
Abstract
Near-infrared spectra from the Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) on Venus Express provide the opportunity for investigating and constraining a wide range of atmospheric parameters for Venus.
The aim of this work is to exploit the wealth of data available from Venus
Express to better understand the behaviour of the Venusian clouds, which
are known to play a significant role in the radiative balance of the planet.
Initial work comparing forward models of the 2.3 µm window region (Allen
& Crawford 1984) with VIRTISM-IR data has resulted in a better 4-mode
cloud model for the low- to mid-latitude regions of the planet. Possible
mesoscale variation in the cloud is indicated by a comparison of the data
with values from radiative transfer calculations using branching plots of radiances at two different wavelengths. When the ratio of radiances at 2.53
and 2.4 µm is approximately related to the cloud base altitude, a correlation
between high base altitude and low cloud opacity is observed.
Further goals are to further investigate the differences found by Wilson
et al. (2008) in the cloud structure in the polar regions, examine the effects of
variations in the composition and size of cloud aerosol particles, and look for
evidence of the sub-cloud haze postulated by Satoh et al. (2009). Once the
model is sufficiently advanced, the eventual aim is to use it in conjunction
with the Nemesis radiative transfer and retrieval tool (Irwin et al. 2008) to
study mesoscale variations in the cloud and haze and relate such variations
to dynamics, gaseous abundances and volcanism.
Contents
1 Introduction
1.1 The Planet Venus . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Missions to Venus . . . . . . . . . . . . . . . . . . . . . . . . .
1
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2 The
2.1
2.2
2.3
Venus Express Mission and Data
Venus Express . . . . . . . . . . . . . . . . . . . . . . . . . .
The Visible and Infrared Thermal Imaging Spectrometer . . .
Observations . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 Models of the Venus Cloud Layer
3.1 The Process of Understanding the Venus Clouds . . . . . . .
3.2 Clouds in Radiative Transfer Models . . . . . . . . . . . . . .
3.3 The Current Oxford Cloud Model . . . . . . . . . . . . . . .
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4 Cloud Microphysics
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4.1 Cloud formation on the Earth . . . . . . . . . . . . . . . . . . 12
4.2 Cloud Microphysics on Venus . . . . . . . . . . . . . . . . . . 14
5 Retrieval Theory and Nemesis
16
6 Improving the Oxford A Priori Cloud Model
6.1 Refractive Index Data . . . . . . . . . . . . . .
6.2 Mode 3 Size Distribution . . . . . . . . . . . .
6.3 Acid Concentration . . . . . . . . . . . . . . . .
6.4 Scale Height . . . . . . . . . . . . . . . . . . . .
6.5 Base Altitude . . . . . . . . . . . . . . . . . . .
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7 Mesoscale Variations in the Venus Cloud
7.1 The 2.54 µm Window . . . . . . . . . . .
7.2 Sensitivity Tests . . . . . . . . . . . . . .
7.3 The Branching Plot Method . . . . . . . .
7.4 Retrievals . . . . . . . . . . . . . . . . . .
7.5 Possible Mechanisms . . . . . . . . . . . .
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8 Plan for Future Work
8.1 Summary . . . . . . . . . . . .
8.1.1 Cloud Parameterisation
8.1.2 Cloud Variation . . . .
8.1.3 Volcanism . . . . . . . .
8.2 Timeline . . . . . . . . . . . . .
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List of Tables
1
2
3
4
5
A comparision table for the atmospheres of Earth and Venus
Brief descriptions of the science cases used by Venus Express.
Aerosol particle size distribution as used in the radiative transfer model of Crisp (1986). . . . . . . . . . . . . . . . . . . . .
Aerosol particle size distribution as used in the Oxford radiative transfer model for Venus. . . . . . . . . . . . . . . . . . .
Vertical distribution of the cloud modes in the initial model. .
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List of Figures
1
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A schematic of the VIRTIS optics module . . . . . . . . . . .
Particle number densities in the three size modes obtained
from LCPS data, as presented in Kliore et al. (1986). . . . .
Image of Venus at 2.3 µm, using data from VIRTISM-IR . . .
A simple schematic of how sulphuric acid clouds may form on
venus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A comparison of VIRTISM-IR spectra with model spectra . .
Comparison of scattering parameters generated using two different sets of optical data for H2 SO4 . . . . . . . . . . . . . .
Comparison of scattering parameters generated for four different modal sizes for mode 3 particles . . . . . . . . . . . . .
Comparison of scattering parameters generated for three different H2 SO4 concentrations for mode 3 particles . . . . . . .
Model fits for lower-cloud fractional scale heights of 3–5 . . .
Typical Venus spectrum from 2.1–2.6 µm . . . . . . . . . . .
Contour plot of the sensitivity of an Oxford forward model
spectrum to changes in temperature . . . . . . . . . . . . . .
The effect on the forward model of multiplying the nominal
water vapour profile by factors of a 0.5 and 2.0. . . . . . . . .
The effect on the forward model of varying the cloud base
altitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The inferred variation in base altitude from a branching plot
of 2.53 v. 2.4 µm peak radiance for the observation 0319 00. .
The 2.3 µm radiance for observation 0319 00 and retrieved
relative cloud opacity, base altitude and relative gaseous abundances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A simple representation of how cloud base variations may
occur on Venus. . . . . . . . . . . . . . . . . . . . . . . . . . .
A Gantt chart representation of my thesis plan. . . . . . . . .
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1
1.1
Introduction
The Planet Venus
Venus is a rocky planet of approximately the same size as the Earth, but
orbiting the Sun at ∼0.72 of the Earth’s orbital radius. It has an orbital
period of 224 days, and a retrograde rotation with a period of 243 days. Its
slow rotation results in atmospheric dynamics very different to those on the
Earth.
The estimated surface temperature of a Venus in radiative equilibrium
with incoming solar radiation would be ∼240 K, slightly cooler than that of
the Earth. However, Venus has a massive atmosphere with a surface pressure
of 90 bars, and the atmosphere is composed largely of carbon dioxide which
is highly absorbing in the infrared, creating an efficient greenhouse effect.
The resulting average surface temperature is closer to 740 K.
Venus is covered in a layer of cloud from ∼48–75 km. This cloud is
thought to be composed of concentrated sulphuric acid droplets, although
the precise composition is still uncertain. The cloud layer contributes to
the extremely high bolometric albedo of Venus, which is ∼0.7. Ultraviolet features indicate the presence of an ultraviolet absorber, thought to be
present at the same altitude as the cloud top. However, so far all attempts
to identify the substance responsible have been unsuccessful.
The slow rotation of Venus results in an atmospheric super-rotation.
Zonal wind speeds in the troposphere and mesosphere of up to 90 ms−1
have been recently inferred from the temperature field as measured by the
Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) on Venus
Express by Piccialli et al. (2008). The mechanism for this super-rotation is
still not understood. Above 100 km, solar heating creates a strong diurnal
temperature gradient which results in a strong sub-solar – anti-solar flow.
Meridional transport is dominated by a Hadley cell between the equator and
∼50◦ latitude. The meridional extent of the Hadley cell has been inferred
from an observed decrease in cloud top altitude at ∼50◦ (Titov et al. 2008).
This conclusion is supported by the observed increase in the concentration of
carbon monoxide at 35 km altitude and ∼60◦ latitude, caused by a downward
transport of CO-rich air with the downwelling branch of the Hadley cell
(Tsang et al. 2008b), although this may be an over-simplistic interpretation
as some longitudinal CO variation has also been observed (Tsang et al. 2009).
Atmospheric vortices that are most often dipolar in shape have been
observed close to both poles, and these are thought to be driven by the
meridional Hadley cell transport. They are characterised by infrared-bright
double-eye features (Piccioni et al. 2007). The north polar dipole structure was first imaged in the far-infrared by the VORTEX instrument on
Pioneer Venus (Taylor et al. 1979). The south polar vortex has been observed by VIRTIS in recent years, and found to be similar to that in the
1
northern hemisphere, although displaying a faster rotation speed (Piccioni
et al. 2007). During the first few months of observation by VIRTIS the
shape remained broadly dipolar, although a detailed double-eye structure
was not always observed (Piccioni et al. 2007). The shape of these vortices
has then been observed to vary between observations, and the exact mechanism for their formation is poorly understood. Similar vortices on Titan
are thought to act as a mixing barrier in the stratosphere and mesosphere
(Teanby et al. 2008), and it is possible that such considerations apply on
Venus.
Venus has a much higher abundance of CO2 , CO and SO2 than the Earth,
but its atmosphere is much dryer. A comparison is provided below in Table
1, with values taken from Taylor & Grinspoon (2009). The reasons for these
compositional differences are unclear, particularly if the initial atmospheres
of Earth and Venus were identical in composition, but it is thought that the
relatively high abundance of SO2 is due to high levels of volcanic activity.
Donahue et al. (1982) interpret the high deuterium-hydrogen abundance
ratio as measured by the Pioneer Venus large probe mass spectrometer as
evidence that Venus was once much wetter than it is today. The D/H ratio
is enriched by a factor of 100 compared to that on Earth, and Donahue
et al. (1982) postulate that this came about from the greater likelihood of
exospheric escape of hydrogen over the heavy isotope deuterium. The high
enrichment indicates that a large amount of hydrogen from the dissociation
of H2 O has escaped from Venus in the past, and this is why Venus is dry.
The low abundance of atmospheric CO2 on Earth compared to that of Venus
could be explained by the high uptake of CO2 by the oceans on Earth and
the subsequent formation of carbonate minerals.
Venus
0.96
0.035
trace
0.000030
0.00015
0.00004
92 bar
∼740 K
CO2
N2
Atomic O
H2 O
SO2
CO
Surface Pressure
Surface Temperature
Earth
0.003
0.770
trace
∼0.01
0.2 ppb
0.12 ppm
1 bar
∼290 K
Table 1: A comparison table for the atmospheres of Earth and Venus. Abundances are taken from Taylor & Grinspoon (2009), and are given as fractions
unless otherwise specified.
Venus has the greatest number of ‘volcanic’ topographic features in the
solar system, and areas of high surface emissivity have also been interpreted
as evidence of lava flows. Radar-bright features from ground-based measure2
ments were interpreted as volcanic in origin by Saunders & Malin (1977), and
the topographical maps generated using data from the Magellan probe have
provided evidence that over 90% of the surface is covered by features that
bear a close resemblance to volcanic features on Earth (Head et al. 1992).
With data from VIRTIS, correlations between high emissivity regions and
volcanic features interpreted from Magellan topography data have been observed (Helbert et al. 2008). Whereas the presence of past volcanism on
Venus is widely accepted, it is unknown whether it occurred in sporadic
bursts of high activity or continuously. Bullock (1997) completed evolutionary model simulations of both possibilities, and concluded that the most
likely evolutionary scenario was an epoch of massive volcanic plains emplacement between 600 and 1100 million years ago, although this has been
debated. Esposito et al. (1988) suggest that an observed decrease in sulphur dioxide concentration above the cloud tops during the Pioneer Venus
mission could be evidence that volcanic activity has occurred more recently,
possibly favouring a more constant outgassing model.
The relationship between the atmosphere of Venus and the surface mineralogy is still unknown. Hashimoto & Abe (2005) discuss the relative merits
of carbonate and pyrite models for surface-atmosphere equilibrium. The
carbonate model is based on the Urey equilibrium reaction (Urey 1952) as
proposed by Bullock & Grinspoon (2001). This carbonate buffer reaction is
CaCO3 + SiO2 ⇀
↽ CaSiO3 + CO2 .
(1)
However, Hashimoto & Abe (2005) believe that the amount of carbonate
rock reservoir required to buffer a 90 bar atmosphere of CO2 would be
equivalent to a layer 1 km thick across the entire surface of Venus. Instead,
they suggest that a pyrite equilibrium model may be more appropriate:
3FeS3 + 16CO2 ⇀
↽ Fe2 O4 + 6SO2 + 16CO.
(2)
As the composition of the surface rock is still unknown, however, reaching
a conclusion as to the precise nature of surface-atmosphere interaction on
Venus is difficult.
Venus has no significant intrinsic magnetic field, so the solar wind interacts directly with the upper atmosphere. MAG and ASPERA instruments
on Venus Express will be used to investigate this interaction and the Venus
plasma environment during the mission (Zhang et al. 2006).
1.2
Missions to Venus
The Venus Express satellite, launched in November 2005, is the latest in
a series of successful missions to Venus that began with the flyby of the
NASA Mariner 2 spacecraft in 1962. Mariner 2 data provided an indication
that temperatures at the surface reached at least 700 K. Several probes
3
from the USSR successfully entered the atmosphere of Venus during the
late 1960s, culminating in Venera 7 becoming the first probe to send a
signal back from the surface of another planet. The Venera series during
the 1970s provided the first in-situ data from the surface and atmosphere
of Venus, including initial surface rock-type indications from radioactive
species abundance, relative abundances of atmospheric constituents, initial
cloud profiles and wind speed data, and confirmation that the solar flux at
the surface is sufficient for a runaway greenhouse to exist (Marov 1978).
The success of these missions was followed by results from the Pioneer
Venus multiprobe and orbiter mission in 1978. Collated data from this mission refined the temperature structure and atmospheric gaseous abundances
obtained by the Venera probes 4–10, and also detected two regions of instability in the atmosphere where overturning can occur from 20–29 km and
52–56 km altitude (Donahue 1979). Data from orbiting infrared and ultraviolet spectrometers and the cloud polarimeter, the nephelometers, the
cloud particle size spectrometer and the solar flux radiometer on the descent
probes provided constraints on cloud structure and particle size. Surface topography was also observed using a radar instrument on the orbiter.
Data from these probes, combined with results from the Venera series,
formed the basis for the Venus International Reference Atmosphere (Kliore
et al. 1986), which is still used as an a priori for Venus atmospheric models
today.
The 1985 Vega 1 and 2 lander/balloon probes close to the equator and
morning terminator provided surface temperature and pressure values of
733 ± 1 K and 89 ± 1 atm respectively, as well as detecting a temperature
inversion between 62 and 64 km (Petropoulos & Telonis 1988). The aim of
the next mission to Venus, Magellan, was to gather radar and radiometric
data from the surface in order to generate a topographical map of Venus.
It also carried a gravity experiment to map the gravity field of Venus and
look for anomalies that may provide an insight to the tectonic structure of
the planet.
A ground-breaking discovery by Allen & Crawford (1984) opened up
new possibilities for remote sensing of the clouds and lower atmosphere
of Venus. Ground-based observations of Venus using the Anglo-Australian
Telescope revealed the presence of ‘windows’ in the infrared within which
the optical thickness of the Venusian atmosphere is sufficiently low that the
lower atmosphere and the surface can be observed remotely.
The Venus Express orbiter is the most recent mission to Venus, and is
the first to exploit these infrared spectral windows to observe the lower atmosphere from space. The varied instrumentation of this mission reflects
its multiple goals. Of particular interest and relevance to this work is the
Visible and InfraRed Thermal Imaging Spectrometer, VIRTIS, which is designed to provide data for surface mineralogy, cloud properties, temperature
and gaseous abundances from the surface to the upper atmosphere.
4
2
2.1
The Venus Express Mission and Data
Venus Express
Venus Express (VEX) was launched in November 2005 and entered Venusian
orbit in April 2006. The nominal mission was due to last for 2 Venus sidereal
days, but has now been extended until December 2009. Seven science instruments are onboard VEX. These are the Analyser of Space Plasma and Energetic Atoms (ASPERA), a magnetometer (MAG), the Planetary Fourier
Spectrometer (PFS, not useable due a a scanning fault), SPectroscopy for
Investigation of Characteristics of the Atmosphere of Venus (SPICAV), the
Venus Radio Science Package (VeRa), the Visible and InfraRed Thermal
Imaging Spectrometer (VIRTIS), and the Venus Monitoring Camera (VMC).
Data from VIRTIS has been used in this work and the instrument is described below in more detail.
2.2
The Visible and Infrared Thermal Imaging Spectrometer
VIRTIS was originally designed for the cometary mission Rosetta, to study
the mineralogy and petrology of the comet P\Wirtanen (Coradini et al.
1998). It consists of three unique data channels, two of which are mapping
channels, one operating in the wavelength range 0.25–1.0 µm (VIRTISMVIS) and the other in the range 1.0–5.0 µm (VIRTISM-IR). The spectral sampling of VIRTIS-M is 0.01 µm. The third channel is devoted to
spectroscopy, and is a high-resolution echelle spectrometer operating in the
range 2.0–5.0 µm (VIRTIS-H). The work presented here uses data from the
VIRTISM-IR channel. A schematic of the instrument taken from Coradini
et al. (1999) is shown in Figure 1.
Data from the VIRTIS-M part of the instrument is transmitted as a
three-dimensional cube, with two spatial dimensions and one spectral dimension. The spectrometer slit is 256 pixels across, and during each observation VIRTIS-M scans in a direction perpendicular to the orientation of
the slit, recording a 256×256 pixel image. The third dimension of the cube
is provided by the 432 spectral channels (Drossart et al. 2007). Geometry
files are also distributed with the calibrated data, which contain geometrical
data for each individual pixel. The instantaneous field of view of VIRTIS-M
over the whole slit is 0.25×64 mrad, which corresponds to a distance of ∼1/3
of the diameter of the planet at apocentre. After taking into account scanning by the secondary mirror, the total field of view is 64 mrad (Drossart
et al. 2007). The spectral resolution of VIRTIS-M is given by Svedhem et al.
(2007) as (λ/∆λ) ∼200, and the size of a single pixel is 0.25 mrad. This
corresponds to a spatial resolution of ∼20 km even at apocentre (60,000 km
from the planet).
Ten modes of observation, or science cases, were developed for Venus
Express during the mission preparation. These are described in detail by
5
Figure 1: A schematic of the VIRTIS optics module, taken from Coradini
et al. (1999).
Titov et al. (2006) and are listed below in Table 2. Out of these ten scenarios,
VIRTIS is operational during cases #1, #2, #3 and #7. VIRTIS-H will be
used for high resolution pericentre observations in case #1. VIRTIS-M will
mainly be operational in cases #2, #3 and #7. Observations in case #7
with VIRTIS-M are in slit mode only, so no scanning is used (Drossart
et al. 2007).
Case #1
Case #2
Case #3
Case #4
Case #5
Case #6
Case #7
Case #8
Case #9
Case #10
Pericentre observations
Off-pericentre observations
Global spectro-imaging from apocentre
VeRa bi-static sounding
Stellar occultation by SPICAV
Solar occultation by SPICAV/SOIR
Limb observations
VeRa Earth radio occultation
VeRa solar corona experiment
VeRa gravity experiment
Table 2: Brief descriptions of the science cases used by Venus Express.
2.3
Observations
24 observations in total were investigated in this work, obtained from eight
different orbits. These observations were chosen because they are the only
6
observations available that have an integration time of 18 s, the longest integration time used by VIRTIS-M. These observations cover southern hemisphere latitudes from 0 – >80◦ , and also cover a range of viewing angles.
Data investigated came from observations 00, 01 and 02 from the orbits
0319, 0320, 0321, 0334, 0344, 0359, 0373 and 0382. As three observations
from each orbit were studied, there is the potential to study the evolution
of particular features from observation to observation within an orbit.
3
3.1
Models of the Venus Cloud Layer
The Process of Understanding the Venus Clouds
The clouds on Venus play an extremely important role in the energy balance
of the atmosphere, and so understanding them is of vital importance if
we are to comprehend the evolution of the Venusian climate. The high
albedo (reflectivity) of the clouds prevents much of the solar radiation from
penetrating as far as the surface, and the sulphuric acid aerosol particles
that form the clouds are also strong scatterers in the near-infrared and strong
absorbers at wavelengths above ∼3 µm, contributing to the greenhouse effect
by preventing thermal radiation from the surface from escaping into space.
After brightness temperatures derived from microwave observations provided initial evidence that the surface temperature of Venus was at least
600 K (Sagan 1960), Sagan (1962) discussed the possibility of a greenhouse
model for Venus, having postulated that water vapour clouds were partially
responsible for this effect (Sagan 1960). Evidence of a stronger compositional candidate for the cloud began to emerge a decade later, when Young
(1973) summarised the inferred properties of the cloud particles from optical
polarisation data. He concluded that the only substance consistent with the
available spectroscopic and polarimetric data was concentrated sulphuric
acid vapour, containing about 75% by weight H2 SO4 . Young also pointed
out that the presence of sulphuric acid is to be expected on a planet with
a high level of volcanic activity, as it is a naturally-occurring constituent of
volcanic gas and can also be formed from other outgassed substances (water
and SO2 ). He concluded that other suggestions such as the acids HCl, HF
and HNO3 could be ruled out, at least as candidates for the upper cloud
layer.
This conclusion is supported by the work of Pollack et al. (1974), who
interpreted reflectance spectra in the 1.2–4.1 µm wavelength region as also
indicative of a sulphuric acid cloud layer. Pollack et al. compared Venus
reflectance spectra with synthetic spectra for several possible candidates and
determined that the only substance that matched a cloud absorption feature
between 3 and 4 µm was a solution of H2 SO4 , with a concentration of 75
% by weight or higher. It was, however, not possible to distinguish between
solutions of 75 and 95 wt % using these data. The possibility of impurities
7
being present in the aerosol particles was invoked to explain a poor match
between H2 SO4 synthetic spectra and data in the ultraviolet region of the
Venus spectrum.
The Pioneer Venus mission, described in detail by Colin (1980), had a
range of instruments on an orbiter and several descent probes devoted to
studying the Venusian cloud. These were the nephelometers on the large
and small descent probes (LN/SN), the Large Probe Cloud Particle Size
Spectrometer (LCPS) and the Orbiter Cloud PhotoPolarimeter (OCPP).
The five descent probes entered the atmosphere at different locations. These
consisted of three small probes, one entering the dayside (Day) atmosphere,
one the nightside (Night) and the third entering the atmosphere at around
60◦ latitude in the northern hemisphere (North). A large probe (Sounder)
and the bus on which the probes were mounted also entered the atmosphere.
The cloud vertical profiles obtained by these probes were generally in good
agreement with similar profiles derived from backscattering nephelometer
data from the Venera 9, 10, 11, 13 and 14 probes, although some variations
in the cloud base and cloud top regions were noticeable (Kliore et al. 1986).
The LCPS instrument provided a vertical profile of the cloud, distinguishing between three different aerosol particle size modes. These modes
range from mode 1, the smallest, to mode 3, the largest. Kliore et al. (1986)
includes a plot, reproduced below (Figure 2), of the vertical distribution of
these three particle modes at the LCPS descent site.
Figure 2: Particle number densities in the three size modes obtained from
LCPS data, as presented in Kliore et al. (1986).
The question of possible impurities in the cloud particles was revisited after results from the Pioneer Venus mission became available. Cimino (1982)
examined data from the radio occultation experiment, and modelled the
aerosol particles as a solid dielectric sphere with a coating of liquid sulphuric acid. This increases the absorptivity of the particles compared to a
8
pure sulphuric acid sphere. The mass contents she derived from the radio occultation data, assuming liquid concentrated H2 SO4 aerosols, are more than
an order of magnitude greater than mass contents determined by the LCPS,
which suggested that particles with a higher absorptivity were required. The
spectral dependence of the absorption coefficient determined for the occultation data was also found to be different from that of liquid H2 SO4 . She
concluded that the best-fit model consisted of a solid core making up 97 %
of the particle by radius, with a thin coating of liquid H2 SO4 .
It is now known that the cloud opacity is highly variable, so a cloud mass
content observed at one time and in one place could very conceivably differ
by an order of magnitude from a content observed elsewhere. However, we
cannot yet rule out the possibility of impurities in the cloud particles as the
nature of the ultraviolet absorber in the cloud top regions remains unknown.
The composition of the largest cloud particles in the lower cloud is also a
subject of debate. Esposito et al. (1983) suggested chlorides such as HCl or
FeCl3 instead of H2 SO4 , or NOHSO4 .
Current observations by VIRTIS allow the study of the Venusian cloud
using the infrared window regions discovered by Allen & Crawford (1984)
between 1.0 and 2.6 µm. Radiance at these wavelengths is heavily attenuated by the cloud and as such measurements at these radiances provide a
good indication of cloud opacity (Figure 3). It has become apparent that
alterations in mean particle size and base altitude can also have a significant effect on the measured spectra from Venus (Carlson et al. 1993, Wilson
et al. 2008, Satoh et al. 2009). The cloud can also be sounded using the
VMC, which monitors the cloud top in the ultraviolet and VeRa, which
provides radio occultation profiles of the neutral atmosphere. A schematic
diagram of the Venusian cloud is given in Figure4.
3.2
Clouds in Radiative Transfer Models
A detailed cloud model, based on data from the OCPP, LCPS and Solar
Flux Radiometer was used by Crisp (1986) in his radiative transfer model
of the Venus atmosphere. His cloud model consists of four H2 SO4 aerosol
particle modes, with radii for each mode listed in Table 3. An upper haze is
present between 80 and 90 km, the upper cloud above ∼ 57 km has a bimodal
distribution of mode 1 and mode 2 particles, and the lower cloud from ∼
48–57 km has a trimodal particle distribution of modes 1, 2 and 3 (mode 2’
is treated as a tail of the mode 2 size distribution but is restricted to the
middle and lower cloud layer). The ultraviolet absorber is incorporated into
the mode 1 particles in the upper clouds.
Crisp’s cloud model is characterised by a lower cloud for which aerosol
particle abundance does not decrease noticeably with height, and an upper
cloud with a scale height of the same order as the atmospheric scale height.
These vertical distributions and size distributions are based on the inter9
Figure 3: An image of Venus at 2.3 µm, plotted using VIRTISM-IR data
from the observation 0319 00. The data have been coadded spatially in bins
of 20 × 20 pixels, at 10 pixel intervals. Blue corresponds to thick cloud and
low radiance, whilst red indicates thin cloud and high radiance.
Mode
Mode 1
Mode 2
Mode 2’
Mode 3
Effective Radius at Equator (µm)
0.49
1.18
1.40
3.65
Eff. Rad. at Poles (µm)
0.29
1.01
1.40
3.65
Table 3: Aerosol particle size distribution as used in the radiative transfer
model of Crisp (1986).
pretation of results from the Pioneer Venus OCPP and LCPS experiments,
data from both being used to constrain optical depths for the upper cloud
and LCPS data being used for the lower cloud.
This model was further developed by Pollack et al. (1993), incorporating
data from the Galileo/NIMS flyby. In their model spectra for the nightside of
Venus, mode 2 particles are restricted to the upper cloud only, whilst mode
2’ and mode 3 are restricted to the lower cloud. Opacity profile modifications
were made in order to bring the model into better agreement with the NIMS
data.
A similar parameterisation was produced by Grinspoon et al. (1993).
They generated a best-fit vertical cloud model by comparing synthetic limb10
darkening curves with those obtained from the Galileo/NIMS data. They
found that the data were fit best by a model in which the upper cloud optical
depth remains constant, and the majority of the cloud opacity variation
occurs in the region from 48–50 km. The results from Grinspoon et al.
(1993) and Pollack et al. (1993) are similar, and favour a three- or fourmode cloud model with larger mode 3 particles towards the bottom of the
cloud. The nominal cloud base is given in Pollack et al. (1993) as 48 km.
Further evidence for a cloud base of ∼48 km is provided by the Pioneer
Venus descent probe results, as summarised in Kliore et al. (1986), and in
Mariner 10 data reanalysed by Kolodner & Steffes (1998).
All three models described above used refractive index data for sulphuric
acid obtained from laboratory measurements by Palmer & Williams (1975).
These data were used, together with the assumed size distributions, to calculate the extinction coefficient and single scattering albedo for each mode
at each wavelength. The derived scattering properties were then included
in the radiative transfer model. Grinspoon et al. (1993) used values 84.5
and 95.6 wt % H2 SO4 as opposed to the 75 wt % used by Crisp (1986) and
Pollack et al. (1993). Palmer & Williams (1975) provide optical data for
these three concentrations. Distinguishing between different concentrations
of acid using observational data is not straightforward as the problem is
underconstrained.
There are other sources of uncertainty for such models. No data was
available between the cloud top and the 75 mbar level at the time of Crisp’s
model, mode 1 particles were too small to be detected by the LCPS instrument, and the extrapolation of a model based on descent probe data
to a planet-wide scale is based on the potentially flawed assumption that
the conditions at the probe entry site and time were typical. However,
the Galileo/NIMS data provided an opportunity to refine this model using remote-sounding data obtained over a wider area of the planet, and
went some way towards removing these uncertainties. The Crisp model as
refined by Pollack et al. (1993) and the model of Grinspoon et al. (1993) together gave the most accurate representation of the Venusian cloud that was
possible with the data available at the time, showing significant agreement
despite different approaches, and therefore these models have been used as
a starting point for those developed in this work.
New possibilities were opened up with the data obtained by Venus Express. Satoh et al. (2009) postulate that there may be small haze particles
as low in the atmosphere as 30 km, based on a best-fit forward model of the
shape of the 1.74 µm peak, but if so these particles cannot be made of concentrated sulphuric acid as sulphuric acid vapour is expected to decompose
into SO3 and H2 O at temperatures found below 45 km altitude on Venus
(Prinn 1978). Also, the possibility of alterations in the average particle size
across the planet is explored by Wilson et al. (2008), after initial findings
by Carlson et al. (1993). They find that the ratio of the peak radiances at
11
1.74 and 2.3 µm is indicative of a ‘size parameter’ for a cloud model with a
single-mode size distribution. When the results of this model are compared
with VIRTISM-IR data, they find that the average particle size is constant
over the majority of the planet but increases towards the poles, indicating
that cloud formation processes are different at latitudes greater than 60◦ ,
possibly as a result of a different convective regime. Erard et al. (2009) suggest that their independent component analysis of VIRTIS spectra indicates
variation in particle size within the polar region, with regions of different
average particle size forming concentric rings around the polar vortex.
3.3
The Current Oxford Cloud Model
The current cloud model in use at Oxford is based on the model of Pollack
et al. (1993), with a few modifications (detailed in Section 6). It has four
particle modes and, as with Pollack et al. (1993), restricts modes 2’ and 3 to
the lower cloud and mode 2 to the upper cloud. The size distribution is given
in Table 4, and all modes are treated as having a log-normal distribution, as
in Pollack et al. (1993). The refractive index data used to generate scattering cross-sections and extinction coefficients is that of Palmer & Williams
(1975). A composition of 75 wt % H2 SO4 is assumed for all size modes.
This choice of concentration is the same as that of Pollack et al. (1993),
Kamp & Taylor (1990), Meadows & Crisp (1996) and Marcq et al. (2005),
facilitating comparison of the models. However, the results of Grinspoon
et al. (1993) favour a higher concentration, which cannot be ruled out and
requires further investigation.
Mode
Mode 1
Mode 2
Mode 2’
Mode 3
Effective Radius(µm)
0.30
1.00
1.40
3.65
Width of Distribution (µm)
0.44
0.25
0.21
0.25
Table 4: Aerosol particle size distribution as used in the Oxford radiative
transfer model for Venus.
4
4.1
Cloud Microphysics
Cloud formation on the Earth
Cloud formation on the Earth can be used as a useful illustration for the
sort of physical processes that may cause the formation of cloud on Venus.
Cloud formation on the Earth relies on convective processes. Parcels of moist
air rise due to convection in the atmosphere, and when the temperature of
such a parcel falls below the dew point temperature it reaches saturation
12
with respect to water (Rogers & Yau 1989). Once saturation is achieved,
water vapour can condense out and form cloud droplets, provided there are
sufficient cloud condensation nuclei.
Adiabatic expansion/contraction of dry air can be described using the
first law of thermodynamics. In differential form, this can be stated as
dq = cp dT − αdp,
(3)
where dq is the change in heat per unit mass, cp is the specific heat capacity
for constant pressure, T is temperature, dp is change in pressure and α is
the volume per unit mass. For an adiabatic process, we can set dq to zero.
If, however, the air is not dry but moist, we have to take into account the
effect of water on these processes. When water is in the vapour phase, we
can treat it as an ideal gas (Rogers & Yau 1989), so we can use the equation
of state for an ideal gas to define the vapour pressure, e:
e = ρv Rv T,
(4)
where ρv is the density of the water vapour and R v is the individual gas
constant for water vapour.
The evaporation of water requires heat. The latent heat of vaporisation
is the heat energy required to convert a unit mass of water into water vapour,
if there is no change in the pressure or temperature. The latent heat L is
given by
Z
q2
L=
dq = ∆u + es ∆α,
(5)
q1
where e s is the vapour pressure at which the air is saturated with respect
to water vapour and ∆u is the change in internal energy between the two
states. Given that we have assumed T is constant, we can also write this as
Z q2
dq
L=T
= T ∆s,
(6)
q1 T
where s is the entropy per unit mass. Equating (5) and (6) allows us to find
a conserved thermodynamic quantity that we will call the Gibbs free energy
G:
G = u + es α − T s.
(7)
Conservation of the differential dG leads to the Clausius-Clapeyron equation, given below:
∆s
L
des
=
=
.
(8)
dT
∆α
T ∆α
The saturation vapour pressure defines the point at which condensation of
water vapour is energetically favourable, and the Clausius-Clapeyron equation gives the temperature dependence of this quantity. Thus, the predominant mechanism on the Earth for creating supersaturations is cooling.
13
However, this rather simplistic model does not entirely describe the full
requirement for cloud formation. The Clausius-Clapeyron equation does
not take into account the free energy barrier for condensation of water into
small droplets (Rogers & Yau 1989), so in fact condensation into droplet
form might not be expected to occur until large supersaturations of water
vapour are reached. In reality, we do observe the formation of cloud particles
for small supersaturations because the air is full of micron and sub-micron
particles that act as a source of cloud condensation nuclei (CCN), facilitating
droplet formation without the need for large supersaturations.
The saturation vapour pressure for a spherical droplet is dependent on
the radius of curvature, and is given below by the Kelvin equation:
2σ
es (r) = es (∞)exp
,
(9)
Rv ρ l T r
where r is the radius of curvature of the droplet, σ is the surface tension and
ρl is the density of the liquid. A droplet must therefore achieve a critical
size if it is to be stable, as the vapour pressure must equal this saturation
vapour pressure for the rates of evaporation and condensation to be balanced (Rogers & Yau 1989). Particles greater than this size are said to be
‘activated’ and it is favourable for them to grow by condensation. Formation of droplets of the critical size can occur by a variety of processes, listed
by Houze, Jr. (1993). The growth of a drop of pure water by condensation
alone is homogeneous nucleation, whereas the growth of a droplet around
an aerosol particle is heterogeneous nucleation. Heterogeneous nucleation is
by far the more important of these two processes on Earth. Cloud droplets
can also grow when smaller droplets collide and coalesce, which is best modelled as a discrete process called stochastic collection. This model results in
a more realistic size distribution than an assumption of continuous growth
as it takes into account the possibility that two drops of the same initial
size may not attain the same size after a time ∆t, as they may experience
different numbers of collisions.
4.2
Cloud Microphysics on Venus
The mechanisms for cloud formation on Venus are poorly understood compared with those on Earth, but the theory above can still be applied. A
very simple cloud formation process for Venus is outlined in Figure 4.
A multi-modal distribution as observed in the Venus cloud favours a
stochastic collection model for the initial growth and activation of cloud
droplets. Knollenberg & Hunten (1980) suggest that the smallest mode 1
particles have not yet reached the critical radius and are not yet activated,
so remain small as they can only grow by coalescence, whereas mode 2
particles have achieved this critical radius and so can grow to larger sizes
more easily, explaining the marked difference in average size between these
14
Figure 4: A simple schematic of how sulphuric acid clouds may form on
Venus. A) marks the upper haze, B) is the upper cloud composed of mode
1, mode 2 and UV absorber particles, and C) is the lower cloud made mostly
of mode 2’ and mode 3 particles, as described by Crisp (1986) and Pollack
et al. (1993).
two modes. Cloud condensation nuclei are believed to be an important
part of this process - indeed, Knollenberg & Hunten (1980) suggest that
the smallest mode one particles detected by the Pioneer Venus LCPS in
the lower cloud may be just bare CCN, with little sulphuric acid content.
Imamura & Hashimoto (2002) assume the CCN to be made of elemental
sulphur, with a single radius of 0.17 µm, based on the LCPS measurements
discussed by Knollenberg & Hunten (1980).
The formation mechanism for mode 3 particles is less certain. Knollenberg & Hunten (1980) suggest that these particles may be crystalline. Other
models treat all modes as composed of concentrated sulphuric acid (see Section 3). The model of Imamura & Hashimoto (2002) results in mode 3-sized
particles being produced by condensation of sulphuric acid as a result of
vigorous diffusion in the region of the lower clouds.
Bullock (1997) in his thesis on the stability of the Venusian climate
utilised a simple chemical and microphysical model for cloud feedback processes. This model took into account the photochemical formation of H2 SO4
aerosols and the subsequent diffusion/convection/condensation processes as
15
shown in Figure 4. A relationship between particle size and number density
was obtained by setting equal the Stokes drift timescale of the particles and
the Brownian coagulation timescale of aerosols. The aerosol vapour was
assumed to be destroyed at a temperature of 432 K, which occurs around
40 km altitude. The resulting particles were then binned according to size
and composition, and this distribution was used in the radiative transfer
calculations.
McGouldrick & Toon (2007) and McGouldrick & Toon (2008) also implement a microphysical cloud model to investigate the mesoscale spatial
evolution of the Venus condensational clouds. They use the Community
Aerosol and Radiation Model for Atmospheres (CARMA) to investigate the
evolution of ‘holes’ in the cloud and the effect of convection cells and gravity
waves. The use the values of Knollenberg & Hunten (1980) at 40 km as the
CCN input distribution for their microphysical model.
The results of these different microphysical models suggest that simple
microphysical parameterisations can be useful in modelling the behaviour
over time of the Venusian cloud. The work of Knollenberg & Hunten (1980)
provides a good physical basis for a multi-modal cloud as observed on Venus.
In summary, it seems likely that the size distribution on the Venusian cloud
is achieved through stochastic collection followed by preferential condensational growth of larger particles, although this does not rule out the possibility that the mode 3 particles may have an entirely different origin.
5
Retrieval Theory and Nemesis
Remote sensing is an extremely useful method of studying planetary phenomena over large areas and obtaining coverage of these phenomena on
planet-wide scales. In this work, I will be using VIRTIS measurements of
infrared radiation from the surface and lower atmosphere of Venus to derive
properties of the cloud. I will use the radiative transfer and retrieval tool,
Nemesis (Irwin et al. 2008), to create model Venus spectra for the wavelength range of VIRTIS-M in which the window regions discovered by Allen
& Crawford (1984) reside (∼1.0–2.6 µm).
Nemesis (Irwin et al. 2008) was created as a retrieval code that could
be used to model any planet and data from any instrument. The acronym
stands for Non-linear optimal Estimator for MultivariatE spectral analySIS.
It uses a non-linear optimal estimator formalism to find the best-fit forward model to a spectrum for up to four different variables simultaneously,
allowing the solution of an under-constrained problem.
Performing a retrieval involves the generation of a radiative transfer
model using a set of a priori values for various parameters. The model
spectrum generated may be sensitive to some or all of these parameters
in certain wavelength regions. The Nemesis tool uses code derived from
16
RADTRANS to generate radiative transfer models. The input for Nemesis
for Venus currently uses pressure and temperature values from the models
of Seiff et al. (1985) to form vertical profiles of 111 altitude levels, ranging
from the surface to 150 km. Seiff et al. (1985) used collected data from
the Pioneer Venus probes and orbiters and Veneras 10, 12 and 13 to obtain
optimal model profiles. Gaseous abundance vertical profiles are taken from
Kliore et al. (1986), and vertical profiles for four cloud modes are used. The
cloud model is described in more detail in Section 6. Nemesis calculates the
spectral radiance leaving the atmosphere at the desired spectral resolution,
allowing the calculation of forward models to simulate results from a range
of instruments.
Radiative transfer models are calculated by solving the equation of radiative transfer (10) for a given set of initial values for each variable parameter:
Lν = Bν (T0 )τν (0) +
Z
1
Bν (T ) dτν (z).
(10)
τν (0)
In Equation (10), Lν is the resulting spectral radiance after radiation
has passed through an atmosphere from the surface to altitude z. Bν (T0 ) is
the Planck function at surface temperature T0 and wavenumber ν, Bν (T ) is
the Planck function at temperature T for an altitude z, τν (z) is the optical
depth at altitude z and τν (0) is the total optical depth of the atmosphere.
The first term in the equation represents the attenuation of radiation in a
beam from the surface to altitude z by the intervening atmosphere, and the
second term represents radiation emitted by the gas within the beam or
scattered into the beam.
Clearly, the solution to this equation requires knowledge of the strengths
and positions of absorption lines for gaseous constituents in the atmosphere.
If the gaseous absorption for a wavenumber region ν → ν + ∆ν is calculated
by taking into account the exact contribution for each individual absorption
line this is very time-consuming, and as several iterations are required before
the best-fit model is calculated it is very inefficient. Two possible approximate methods can reduce computation time significantly, and these are the
band model approximation and the correlated-k approximation. The band
model approximation cannot be used in a scattering atmosphere, and as the
clouds on Venus are strong scatterers in the VIRTIS wavelength range the
correlated-k approximation, originally used by Lacis & Oinas (1991), is the
only valid option.
The correlated-k approximation assumes that the precise location of an
absorption line of absorption coefficient k within a small frequency interval
ν → ν + ∆ν is of no importance to the calculation of the transmission in
that interval. It is in fact sufficient to know what fraction of the frequency
domain f (k)dk is occupied by absorption coefficients between k and k + dk
(Irwin et al. 1997). Then, the mean transmission within this interval can be
17
written as:
T̄ (m) =
Z
∞
f (k)e(−km) dk
(11)
0
where m is the number of molecules per square metre of atmosphere. Equation (11) has the form of a standard Laplace transform of the frequency
distribution of k, and it is independent of the ordering of the absorption
coefficients. Therefore we can define the cumulative frequency distribution
g(k) =
Z
k
f (k)dk
(12)
0
and if Equation (12) is inverted such that k(g) = g −1 (k) then we can rewrite
T̄ (m) as
Z 1
T̄ (m) =
e(−k(g)m) dg.
(13)
0
If we divide the space between g = 0, 1 into N intervals such that g is
well-sampled, we can then express T̄ (m) as a sum rather than an integral:
T̄ (m) =
N
X
e(−k̄i m) ∆gi .
(14)
i
This is valid for a homogeneous path through an atmosphere. In reality,
such paths are inhomogeneous, and this inhomogeneity can be approximated
by adding homogeneous layers together. The transmission within each layer
is generally well-correlated with the transmissions in adjacent layers, so this
approximation is valid. The name ‘correlated-k’ arises from this fact (Tsang
2007). The distribution k(g) can be calculated and used as an input to the
radiative transfer model, resulting in a fast forward model calculation.
Line strength data for different modes of common atmospheric gases are
obtained from laboratory measurements, although for a planet such as Venus
some degree of extrapolation in temperature and pressure may be required
as the conditions are very different from those on Earth. The correlated-k
tables for Venus are created using data from two main databases (Tsang
et al. 2008a). These are HITEMP, referred to by Pollack et al. (1993) (no
specific publications exist), and HITRAN2K (Rothman et al. 2003). CO2
values from HITEMP are used, as this database contains weak rotational
lines and bands that become important at high temperatures and are absent in HITRAN2K (Tsang 2007). Both Pollack et al. (1993) and Tsang
(2007) find that simulations using HITEMP data are much improved over
simulations using only HITRAN CO2 lines. All other gaseous parameters
are taken from HITRAN2K.
Once the initial forward model is calculated in a retrieval run, an iterative
approach is used to alter a user-specified selection of the input parameters
18
such that an optimal fit to the data is achieved. The best-fit values for each
parameter are then returned.
Non-linear optimal estimation is complex. For a linear problem, we
can represent the measured properties of an atmosphere y, in this case
the radiation emitted at different wavelengths, as some function of a set of
variables such as pressure, temperature, gaseous abundances etc. which we
will call x, plus a term ǫ arising from the measurement errors:
y = F(x) + ǫ.
(15)
If we ignore non-linear terms in F(x), we can write Equation (15) as
y − ya = K(x − xa ) + ǫ,
(16)
where subscript a denotes an a priori vector. This cannot be solved for x
by simple inversion as the problem will suffer from ill-conditioning — errors
in the measured values will propagate and lead to unphysical solutions.
Instead, an optimal estimation method is required. For non-linear optimal
estimation where the problem is close to being linear, the Gauss-Newton
method can be used (Rodgers 2000). This method is valid if the second
derivative of the forward model ∇x KT is small, as in the moderately linear
case, and it provides an iterative solution for x as shown below. The equation
given in Irwin et al. (2008) is
xn+1 = x0 + Sx KTn (Kn Sx KTn + Sǫ )−1 (ym − yn − Kn (x0 − xn )),
(17)
where ym and yn are the measured spectrum and the spectrum calculated
from the trial atmosphere respectively, xn and x0 are the model and a priori
state vectors, Kn is the matrix of functional derivatives, Sǫ is the measurement covariance matrix and Sx is the a priori covariance matrix. The
covariance matrices represent the errors in the measurements and forward
model (Sǫ ) and the errors in the a priori state vector (Sx ).
The difference between the calculated and measured spectra is minimised
when the cost function given by Irwin et al. (2008) is minimised. The cost
function φ is given by
T −1
φ = (ym − yn )T S−1
ǫ (ym − yn ) + (xn − x0 ) Sx (xn − x0 ).
(18)
The matrix of functional derivatives Kn represents the change in radiance at each wavelength for a change in any given input parameter — for
example, a change of 1 ppmv in a gaseous abundance or a 1 K change in
temperature. If a continuous vertical profile of gas or temperature is fitted,
the covariance matrix is an indicator of the sensitivity to the gaseous abundance/temperature at each vertical level and each spectral interval in the
model.
19
Nemesis has the capability to retrieve up to four different variables such
as H2 O abundance, temperature and cloud distribution using various different parameterisations. For example, Nemesis can retrieve a continuous
H2 O vertical profile, or it can simply retrieve a scaling factor for an existing
a priori vertical distribution. In addition, Nemesis can be used to perform
multi-stage retrievals, so one parameter (for example the cloud opacity) can
be retrieved using one part of a spectrum, then this value can be fixed and
another part of the spectrum used to simultaneously retrieve three or four
gaseous abundances. The errors from the first part of the calculation are
taken into account in the second stage.
The Venusian cloud is treated by Nemesis as a collection of highlyscattering spherical particles with a given size distribution. Mie scattering
theory is used to determine the scattering properties of the Venus cloud particles, as the particle size is comparable to the wavelength in the infrared.
The Henyey & Greenstein (1941) approximation to the full Mie-scattering
phase function has been used in the Nemesis calculations to save on computation time. The Henyey-Greenstein phase function approximation used
here is given by
1
1 − g22
1 − g12
P (θ) =
+ (1 − f )
, (19)
f
4π
(1 + g12 − 2g1 cosθ)3/2
(1 + g22 − 2g2 cosθ)3/2
where θ is the scattering angle, f has a value between 0 and 1 and g 1 and
g 2 are asymmetry parameters, measures of the anisotropy of the scattering. The two terms in the equation represent the forward- and backwardscattering peaks respectively.
6
Improving the Oxford A Priori Cloud Model
The cloud model forms a crucial part of any radiative transfer model for
Venus, and a well-constrained cloud model is therefore necessary for retrievals of gaseous abundances below and within the cloud. The 2.3 µm
window region is particularly useful for constraining gaseous abundances, as
the 2.3 µm peak itself is sensitive only to the cloud opacity, whilst the region
between 2.3 and 2.5 µm is sensitive to CO, H2 O and OCS. This means that
the cloud opacity can be constrained independently of the gaseous absorption, which can then be investigated. However, this is of course only useful
if the cloud model is sufficiently realistic.
My initial work has taken the form of improving the current Oxford
cloud model. Problems with this model in the 2.3 µm window region had
become apparent when models with a high input cloud opacity were created.
The shape of the model in this region became distorted with respect to the
observed spectral shape when the number of particles in the lower cloud was
increased (Figure 5).
20
Figure 5: A comparison of data from the VIRTISM-IR observation 0321 02
with radiative transfer models of a similar radiance. A discrepancy in the
behaviour can be seen at 2.47 microns, where the model radiance is too
high for the example with the lower peak radiance and higher cloud amount
(orange lines).
Several possibilities for the cause of the observed discrepancy were investigated. It appears from the plot that there is some significant emission
in the model from the cloud at 2.47 µm when the number density of cloud
particles is high, which could be caused by several factors. Uncertainties are
present in the current a priori values as based on the Pollack et al. (1993)
cloud model, which was discussed in Section 3. Likely errors in parameters
derived from previous observational data that may produce this effect are
as follows:
1. The optical data from Palmer & Williams (1975) shows that the
21
aerosol particles are not completely scattering in the wavelength
range of interest. Large fractional errors in the imaginary refractive
index in this wavelength range may result in an incorrect value for
the calculated single-scattering albedo.
2. An increase in the size of the largest mode 3 particles would alter the
scattering properties of these particles and this may affect the shape
of the spectrum. The exact size of these particles is not well known.
3. Using a different concentration of H2 SO4 for the largest particles
may alter the model spectrum, and the exact concentration is not
well-determined. Previous models have used a range of
concentrations from 75 wt % to 96 wt % (see Section 3).
4. The vertical distribution of the cloud has only been directly
measured by a series of descent probes, which provide information
only for a specific place and time. Whilst different descent probe
profiles show significant agreement, there are also some discrepancies,
as noted by Kliore et al. (1986). Altering the scale height and/or
base altitude of the lower cloud will change the number of cloud
particles present in the line-forming region, which in turn would have
an effect on the emission observed at 2.47 µm.
These possible sources of error were investigated in turn by altering
the relevant input parameters to the model and seeking a solution with a
generally better fit to the data by eye. The initial altitude ranges and scale
heights for the four cloud modes are given below in Table 5.
Mode
Mode 1
Mode 2
Mode 2’
Mode 3
Base Pressure (atm)
1.6
0.116
1.4
1.4
Top Pressure (atm)
0.0017
0.0017
0.389
0.389
Frac. Scale Height
1.0
1.0
1.0
1.0
Table 5: Vertical distribution of the cloud modes in the initial model.
6.1
Refractive Index Data
The process of obtaining laboratory refractive index data for sulphuric acid
aerosol is complex, and therefore the absolute reliability of the Palmer &
Williams (1975) data for use in our cloud model is perhaps questionable.
The uncertainty given for the imaginary part of the refractive index k in
particular is high when k is small, so in the wavelength range of interest this
uncertainty will be significant.
Another set of refractive index data that covers the major window regions
in the infrared is presented by Myhre et al. (2003). These data were used
22
to generate new extinction cross-section and single-scattering albedo values
to use as inputs for a forward model calculation. Myhre et al. (2003) used a
Fourier Transform Spectrometer, unlike the single-beam spectrometer used
by Palmer & Williams (1975) (Rusk et al. 1971). The spectral range used
was also different to that of Palmer and Williams, starting from 1.33 µm as
opposed to 0.63 µm.
The extinction cross-section and single-scattering albedo calculated using
the two data sets for the lower cloud modes are shown below in Figure 6.
It can be seen that the single-scattering albedo is considerably lower for the
Myhre et al. data set towards shorter wavelengths, and this results in an
unrealistically small radiance peak in the 1.74 µm window relative to the 2.3
µm peak when these data are used to calculate a forward model. Using this
new dataset does not improve the quality of our model, and it is possible
that the short wavelength cut-off in these data at 1.33 µm makes the short
wavelength results unreliable.
No other datasets in the correct wavelength range at the correct temperatures and pressures are available.
Figure 6: A comparison of extinction cross-section and single-scattering
albedo generated from two different refractive index datasets by Palmer and
Williams (1975) and Myhre et al. (2003).
6.2
Mode 3 Size Distribution
The precise size distribution for the large mode 3 particles is uncertain, so
it is possible that the discrepancies between our model and the data arise
from this. We know these particles are large compared with the other three
modes, so increasing their modal size from the nominal value (see Table 4)
was another possibility for improving our model.
23
Figure 7: A comparison of extinction cross-section and single-scattering
albedo generated for four different modal sizes for mode 3 particles. Increasing the particle size decreases the single-scattering albedo and extinction cross-section.
Figure 8: A comparison of extinction cross-section and single-scattering
albedo generated for three different concentrations for mode 3 particles.
Slight differences in the region of interest (2.3–2.5 µm) have little effect on
the model spectra produced.
24
This process in fact reduced the goodness of fit for high cloud amount,
as increasing the modal size of the particles decreased the single-scattering
albedo and resulted in an increase in the absorptivity/emissivity (Figure 7).
6.3
Acid Concentration
The concentration of sulphuric acid in the cloud aerosols may be higher
than the 75 wt % value used for the nominal Oxford cloud model, and in
particular this may be different for the largest particles. Pollack et al. (1974)
could not distinguish between a 75 wt % solution and a 95 wt % solution.
Palmer & Williams (1975) also provide refractive index data for 85 and 96
wt % concentrations, so the effect of this on the mode 3 single-scattering
albedo and extinction cross-section was investigated (Figure 8).
The effect of this was insufficient to produce the required improvement
in the spectral shape, and in fact had little effect on the spectrum over the
wavelength range of interest, meaning that any results obtained using this
range are relatively insensitive to acid concentration.
6.4
Scale Height
The initial model test in Figure 5 was completed for a fractional scale height
of 1.00 for all four cloud modes, meaning that the number density of cloud
particles decreased with altitude at the same rate as the number density of
gas molecules in the atmosphere. However, the cloud model of Crisp (1986)
has a lower cloud absolute scale height approaching infinity – in other words,
the number density in the lower cloud does not decrease noticeably with
height. This is borne out by the results from the Pioneer Venus and Venera
descent probe missions (Kliore et al. 1986).
Tests were initially completed with lower-cloud (modes 2’ and 3) fractional scale heights of 3, 4 and 5, significantly increasing the absolute scale
height from the initial model, from ∼6 km to ∼18—30 km. It can be seen
immediately that there is an improvement in the model fit, particularly in
the ratio of a bright spectrum to a dark spectrum, once the scale height is
increased (Figure 9).
Once the scale height is increased to these values there is not a great deal
of variation present in the quality of model fit, which is now much improved.
A fractional scale heights of 4 produces the best quality of fit.
The other method of vertical redistribution of aerosols in the model is
the alteration of the base altitude. Such alteration may be necessary to
produce an optimal fit for both low- to mid-latitude and polar data, which
display somewhat different bright:dark ratio shapes, indicating a different
cloud regime polewards of 60◦ . This would be consistent with the findings
of Wilson et al. (2008) and Titov et al. (2008).
25
Figure 9: Model fits for lower-cloud fractional scale heights of 3–5. The base
altitude is 45 km. The observation is VI0321 00, as above.
6.5
Base Altitude
A range of base altitudes from 43–52 km was investigated to find the best
fit solution. A solution was viable for low- to mid-latitude data, using a
fractional scale height of 4 and a nominal base altitude of 45 km. However,
this was not straightforward for the polar data. It is likely that a failure so
far to take into account possible variations in the average particle size at the
poles is responsible (Wilson et al. 2008). Further progress must be made
before a reliable a priori polar cloud model can be defined.
A small discrepancy at 2.4 µm between the model and data persists,
even for the best fit case. This is particularly noticeable for the bright:dark
spectral ratio. This work on the cloud model has been utilised by Tsang
et al. (2009, in preparation), where it is suggested that this discrepancy is
26
due to a variation in water vapour abundance at ∼35 km that is negatively
correlated with the optical thickness of the cloud. If a decreasing water
vapour abundance with increasing cloud optical depth is introduced into
the models, then for several spectra of varying radiances the model can be
made to fit the data very well.
7
7.1
Mesoscale Variations in the Venus Cloud
The 2.54 µm Window
We observe a small radiance peak just longwards of the 2.3 µm window
complex (shown in Figure 10), lying between 2.50 and 2.58 µm. It is reproduced by our forward model, but its strength appears to be variable in
the VIRTIS data for spectra with the same 2.3 µm peak radiance. Because
the radiance for this peak is ∼1 order of magnitude smaller than the 2.3
µm peak radiance, it can be difficult to distinguish from the noise, which is
of order 10( − 3) W/m2 /sr/µm, so the observations used to investigate this
window region are 24 observations each with an 18 s exposure time.
Because the strength of this window is observed to vary, it provides the
opportunity to constrain a new mode of variability. In particular, variation
in the ratio between the radiances at 2.3 and 2.53 µm can be mimicked
by model spectra with different base altitudes. This window may therefore
provide a constraint on the base altitude, and the observed variation may
indicate that the base altitude is not constant, despite good agreement between the values of ∼46—48 km from the different descent probe datasets
(Kliore et al. 1986).
Before this property can be investigated, sensitivity tests are necessary
to determine which gaseous constituents, if any, the window is sensitive to.
The temperature weighting function will also be a useful indication of the
altitude sensitivity between 2.5 and 2.6 µm.
7.2
Sensitivity Tests
When a retrieval is performed using the Nemesis retrieval code, the functional derivatives of the model parameter(s) of interest are calculated as well
as the forward model radiances for the current values of these parameters.
This is also the case for a single forward model run if the parameter in question is included in the a priori file. If the given a priori for the parameter of
interest is a continuous profile with height, then the derivative is calculated
for each altitude level in the model and for each wavelength interval.
Functional derivatives of temperature are a useful indicator of the altitude sensitivity at any given wavelength. The temperature functional derivative, normalised in each wavelength bin, is shown in Figure 11.
27
Figure 10: The 2.3 µm window. The sensitivities of the small shoulder
between 2.5 and 2.6 µm have not been investigated prior to this work. This
image is a spectrum from the VIRTISM-IR observation 0319 00.
Figure 11: The sensitivity of an Oxford forward model spectrum to changes
in temperature, with wavelength and altitude. Note that the altitude of
maximum sensitivity is higher between 2.5 and 2.6 µm, at about 50 km
(within the lower cloud layer).
28
This figure shows that the 2.5–2.6 µm region is sensitive at an altitude
that we believe lies within the lower cloud. Sensitivity to cloud base altitude
in this region is therefore likely. It is also possible that sensitivity to minor
gaseous constituents at this altitude will allow further constraints on the
vertical profiles of these constituents.
Sensitivity to the gases CO, H2 O, CH4 , OCS, SO2 , HF, HCl and H2 S
has been tested in the region of interest, and the only one of these with
a significant enough contribution for observation with VIRTIS-M to be a
realistic prospect is H2 O. This is interesting, considering the potential of
the 35 km altitude H2 O variation found by Tsang et al. (2009, in preparation) for providing constraints on dynamics and cloud formation processes.
An example set of three forward models in the region of interest for three
different scalings of the H2 O a priori vertical profile is shown in Figure 12.
However, cloud parameters also have an effect on this small window
region. Clearly there is sensitivity to the total cloud optical depth, as in
the other window regions, but from Figure 13 we also see that this region
is sensitive to cloud base altitude. At the resolution of VIRTIS-M, the
effect of water is not distinguishable from the effect of base altitude in this
wavelength region alone. As the effect of base altitude is a grey effect across
this wavelength range it may be possible to use VIRTIS-H to distinguish
between this and water vapour, although the low signal-to-noise ratio is
likely to be problematic. The base altitude is taken to be the base altitude
for mode 2’, which is the main contributor to opacity in the lower cloud.
7.3
The Branching Plot Method
In order to distinguish between the effects of water vapour and cloud base altitude with VIRTIS-M data, it is necessary to use a wider wavelength range
than just the small window between 2.5 and 2.6 µm. The region between
2.3 and 2.5 µm is sensitive to the abundance of water vapour at ∼40 km,
and if we assume that the a priori vertical distribution of water vapour that
we are using represents the real vertical profile well we could in theory use a
comparison between this region and the 2.5–2.6 µm region to simultaneously
constrain both water vapour and cloud base altitude. Clearly, the assumption that the a priori vertical distribution is valid may be flawed, and this
possibility must be investigated further, but for the following work I have
considered the assumption to be valid.
One method that has been used previously to identify modes of variability in the data is the branching plot method. A branching plot is simply a
plot of radiances for one wavelength against another for all the data points
in a single observation. Deviations from a single branch indicate a variable
quantity that produces a different response at the two different wavelengths.
This method has been used by Carlson et al. (1993) and Wilson et al. (2008)
to investigate alterations in the average size of cloud particles.
29
Figure 12: The effect on the forward model of multiplying the nominal water
vapour profile by factors of a 0.5 and 2.0. The presence of a water band at
∼2.55 µm is indicated.
Figure 13: The effect on the forward model of varying the cloud base altitude. The sensitivity drops for a base altitude above ∼51 km.
30
Figure 14: The inferred variation in base altitude from a branching plot of
2.53 v. 2.4 µm peak radiance for the observation 0319 00. Correlation can
be seen between the base altitude and the 2.3 µm peak radiance. The red
lines on the branch plot are second-order polynomial functions, extrapolated
from polynomial fits to forward models created by Nemesis.
A branching plot of peak radiances at 2.53 µm versus peak radiances at
2.4 µm for a single observation has the useful property of being insensitive
to variations in the abundance of water vapour, whilst showing strong variability with changes in base altitude. Forward models with different base
altitudes and optical depths for mode 2’ were generated, based on departures
from the low- to mid-latitude a priori cloud described in Section 6. These
models produce branches for different base altitudes that correspond well to
branches observed in the data, and they can be fit by a second-order polynomial function. This property can then be used to produce quick ‘model’
branches and calculate an approximate value for base altitude for each data
31
point in a branching plot. An example result for this method is shown in Figure 14. It can be seen that there is definite correlation between the radiance
at 2.3 µm and the base altitude, which corresponds to an anti-correlation
between base altitude and cloud optical depth. The correlation coefficient
R2 obtained for VI0319 00 is 0.44.
32
7.4
Retrievals
Whilst the branching plot method is a good first indication that there is
some variability in cloud base altitude and that it is related to the total
cloud opacity, the method fails to take into account possible variations in CO
and OCS abundances, which would alter the radiance at 2.4 µm. Therefore,
to validate this method it is necessary to use Nemesis and perform a full
retrieval.
I created a new parameterisation to enable Nemesis to retrieve the base
altitude of a single cloud mode for a fixed total optical depth. This allowed
me to perform a two-stage retrieval: stage one retrieves the relative optical
depth of mode 2’ with respect to the a priori optical depth using the wavelength range 2.15–2.3 µm, and stage two retrieves the relative abundances of
CO, H2 O and OCS, and the base altitude, using the range 2.3–2.6 µm. Tests
with synthetic noisy spectra confirmed the retrievability of these parameters, although the sensitivity to base altitude drops once it has increased
beyond about 52 km.
In order to perform a retrieval on VIRTIS data, it is important to ensure
that the signal-to-noise ratio is sufficiently high (at least 100) and also that
there is no wavelength offset between the model and data. In order to
achieve sufficient signal-to-noise, a coadding routine is used to average over
squares of 20×20 pixels at intervals of 10 pixels in the 256×256 pixel spatial
dimension of a VIRTIS data cube. Ignoring dark pixels and any squares for
which the signal-to-noise falls below 100, this results in a 25×25 pixel image
for each wavelength bin over the desired spectral range. The noise for each
wavelength bin is calculated as follows:
p
N = Ni / tint npix ,
(20)
where N is the calculated noise, Ni is the instrument noise, tint is the integration time and npix is the number of coadded pixels.
VIRTIS-M has some variation in spectral registration across an image
and has a wavelength offset of ∼+0.008 µm, so the coadding routine also
cross-correlates the spectrum for each pixel against a normalised synthetic
spectrum to remove the wavelength shift before the spectra are coadded.
The retrieval process is ongoing as the input forward modelling errors
and a priori errors must be carefully chosen to optimise the goodness of fit,
as indicated by the reduced χ2 value output by Nemesis. This involves a
significant amount of trial and error, and as the computing time for one
observation is of the order of four days final results will take some time to
complete. However, initial indications from these retrievals are that the base
altitude variation indicated by the branch plot method does exist (Figure
15). The negative correlation between water vapour abundance and relative
cloud opacity as reported by Tsang et al. (2009, in preparation) is observed,
but there is also apparent correlation between areas of very thick cloud and
33
Figure 15: The 2.3 µm radiance for observation 0319 00 and retrieved relative cloud opacity, base altitude and relative gaseous abundances.
34
areas of high relative gaseous abundances. This may be caused by a failure
of Nemesis to produce a good fit in areas of thick cloud, which of course have
lower radiance spectra, but if these areas are still present with sufficiently
low errors and off-diagonal correlation coefficients in the covariance matrix
that are sufficiently close to zero then it may be a real effect.
35
Figure 16: A simple representation of how cloud base variations may occur
on Venus. Arrows indicate the presence of a convection cell. Thick cloud
forms in regions of upwelling as H2 SO4 vapour is transported upwards and
condenses.
7.5
Possible Mechanisms
A possible model for cloud formation has been shown in Figure 4. Figure
16 shows how mesoscale convection may lead to differences in base altitude
that correlate to the cloud opacity. Support for this theory may be found
in the McGouldrick et al. (2008) paper on observations of cloud evolution,
in which they postulate that the formation of holes in the cloud is related
to convection on the scale observed here.
If the correlation between thick cloud and high gaseous abundances is
confirmed, this could be the caused by active volcanism on Venus. All the
gases retrieved here are constituents of volcanic gas, and we might expect
an increase in SO2 from volcanic outgassing to result in an increased level
of cloud opacity. However, these measurements lie within the current error
bars so further work on the retrieval process is needed before these results
can be considered significant.
36
8
Plan for Future Work
8.1
Summary
The topic I have chosen for my thesis is the further study of the clouds
of Venus. Several features of the cloud are poorly constrained and poorly
understood, and as the cloud plays a significant role in the radiative balance
of Venus it is a key area for study. An improved understanding of the
cloud enables the creation of models which better represent the current
atmosphere of Venus, and may also lead to an improved understanding of
the coupling of the clouds with the other atmospheric constituents, dynamics
and geology of Venus. A new cloud parameterisation would therefore have
implications not just for radiative transfer modelling of Venus but also for
dynamical modelling, microphysical cloud modelling, studies of volcanism
and evolutionary modelling. The main goals of this research are to:
1. Implement a new cloud parameterisation that best represents the
meridional and vertical distribution of the cloud, based on data from
the VIRTIS instrument, and relate this if possible to global-scale
dynamics.
2. Examine mesoscale departures from the above distribution and look
for relationships with similar variations in gaseous abundances.
3. Investigate the possibility of observing the effects of volcanic
outgassing on the formation of cloud.
8.1.1
Cloud Parameterisation
I intend to develop the work already completed on the low- to mid-latitude
cloud model by examining the effects on this model of compositional/size
differences in the cloud particles, using the RADTRANS code to generate
forward models for comparison with VIRTIS spectra. I will endeavour to
develop a similar parameterisation for the polar regions. I intend to make
use of a large fraction of the VIRTIS spectral range to do this, particularly
focusing on the windows at 1.74 and 2.3 µm which we know to be highly
sensitive to variations in the cloud. I will also introduce a sub-micron haze
below the clouds as postulated by Satoh et al. (2009) into our model to
examine the effect.
My initial method, which I used in the development of the low- to midlatitude cloud model, will be to look at the ratio of dark and bright spectra
over the 2.3 µm window and attempt to reproduce this with forward models
of similar peak radiances. I will then examine the effect of varying particle
mode sizes, including the 1.74 µm window, as it has been postulated (Carlson
et al. 1993, Wilson et al. 2008, Erard et al. 2009) that the average particle
size changes in the polar regions.
37
I hope to finally have a reliable cloud model that provides a good representation of the planet-wide cloud structure, such that I can relate it to the
dynamics and in particular the meridional Hadley cell transport.
8.1.2
Cloud Variation
Once a general model is in place, I will further develop my work examining
base altitude variations across a single observation. A new base altitude
retrieval parameterisation written for the Nemesis retrieval tool has already
been implemented with some success, and I hope to extend this analysis
to the polar regions and also to the sub-cloud haze. Radiative transfer
modelling and retrievals on these scales would be complimentary to the
microphysical modelling of such variations (McGouldrick & Toon 2007, McGouldrick et al. 2008, McGouldrick & Toon 2008). As it is possible to
co-retrieve up to four parameters in a single run with Nemesis, abundances
of gases can retrieved simultaneously with cloud parameters if the spectral
region used is sensitive to them. This provides the opportunity to look for
similarities in plots of cloud base altitude and plots of gaseous abundances,
which may provide insight into mesoscale dynamics and cloud formation on
these scales. At the time of writing a general model for low- to mid- latitudes
is largely complete, and even if such a general model is not achievable in
polar regions comparisons with the low-latitude model will facilitate further
investigation.
8.1.3
Volcanism
Whilst detection of active volcanism may be possible through the identification of temperature anomalies, it is expected that a new crust would
form rapidly over any volcanic outflow on Venus, leading to very short-lived
hotspots, and therefore “the most sensitive detection could come from subtle variations in atmospheric composition above volcanic plumes or geysers”
(Drossart et al. 2007). Water vapour and SO2 are two of the major components of volcanic gas, and these gases react in the upper atmosphere of Venus
to form sulphuric acid aerosol. Therefore, it might be expected that changes
in the level of volcanic activity on Venus would affect the cloud opacity across
the planet, and local activity may also affect the cloud locally. Variations in
the abundance of SO2 have been observed (Esposito et al. 1988), but so far
have not been accepted as conclusive evidence for current volcanic activity.
Anomalously high amounts of sulphuric acid aerosol may, as on Earth, be
linked to volcanic activity (Baran et al. 1993), and this would be likely to
have an impact on cloud opacity over timescales of a few months. Observations of such alterations in cloud opacity may be possible with VIRTIS
data, and this may provide new evidence for volcanic activity on Venus. I
will also compare any such anomalies with SPICAV/SOIR SO2 abundance
38
measurements from the same period, if obtainable, although a direct comparison may be difficult as SPICAV/SOIR (Bertaux et al. 2007) SO2 data
are for regions above the cloud. Anomalously high values for CO and OCS
may also be indicative of volcanic activity.
39
8.2
Timeline
An approximate timeline is included in the list below, with a Gantt chart
in Figure 17:
January 09–December 09
1. To refine the current best-estimate low- to mid-latitude model.
2. To create a new polar cloud model.
3. To continue the base altitude retrievals for the low- to mid-latitude,
18-second exposure time VIRTIS-M observations.
January 10–May 10
1. To use the new polar cloud model to perform retrievals of base
altitude and gaseous abundances at the poles.
2. To create and implement a general cloud model which takes into
account changes in structure with latitude.
3. To look for variations from this general model on local scales.
4. To look for correlation between such variation and variation of
gaseous abundances.
5. To investigate the sensitivity of the model to changes in cloud
particle composition and size.
June 10–October 10
1. To investigate the effect of adding a sub-cloud haze to the radiative
transfer model.
2. To implement a parameterisation for the retrieval of sub-cloud haze.
3. To look for correlation between any observed spatial variations in the
sub-cloud haze and spatial variations within the main cloud deck.
November 10–March 11
1. To look for variations in cloud opacity and compare with SO2
abundance variations, which may be indications of active volcanism.
2. To examine possible microphysical and dynamical mechanisms for
any phenomena discovered above, possibly with GCM comparisons.
April 11–September 11
1. To make any necessary further refinements to the model.
2. To write up the work. I aim to have completed a study of Venusian
cloud composition, vertical distribution and interaction on both
global and smaller scales.
40
Figure 17: A Gantt chart representation of my thesis plan. Colours refer to
the hierarchy of tasks (purple→red→blue).
41
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